From Longman Dictionary of Contemporary Englishhair's breadthˈhair’s breadth noun [singular] SMALLa very small amount or distance The bullet missed me by a hair’s breadth.
Examples from the Corpus
hair's breadth• Hair's breadth majorities are not enough.• In the United States citizens got one government rather than another by a hair's breadth.• I came within a hair's breadth of losing my life.• Their stories appear to rupture time, bringing them within a hair's breadth of one another. 